Momentum, Collisions and Explosions Legacy Problem #4 Guided Solution

You'll find that oftentimes in physics, a problem is not so much mathematically difficult as it is conceptually difficult. The mathematical operations that have to be performed are rather straightforward and simple, but the conceptual reasoning that has to be done is much more difficult. That might be the case here in this problem, in which Jerome, our middle linebacker, delivers a big hit to the other team's running back during the game this past weekend. Now what we observe is that the running back had a mass of 82 kilograms and was moving east at 5.6 meters per second. You're asked to determine the pre-collision momentum on the running back. That's simply mass times velocity to get momentum. 82 times 5.6 would give you that answer. Now it comes out to be about 459 kilograms times a meter per second. We'll round that to 460 to have two significant digits, and we'll recognize that that's an eastward momentum, consistent with the fact that the running back is running east. Now after the collision, that running back got turned around and was moving back the opposite direction, west, at 2.5 meters per second. So the momentum after the collision is the mass, 82, times 2.5. Now that's not mathematically difficult. You can do that. When you do it, you get 205 kilograms times a meter per second. We can round that to two digits, it becomes 210 kilograms times a meter per second. Now what we have to do in the next part of the problem is we have to determine the momentum change in the running back. It was moving east and then later is moving west. And so the change goes from a positive 459 to a negative 205. And when you compute the change on that, it comes out to be 664 kilograms per meter per second. The direction of the momentum change could be considered to be west, because after all, when you do final momentum, after collision momentum, minus the initial momentum, you're doing a west minus an east. Now you could call the west a negative value, and so you're doing negative 210 minus 460, better yet, negative 205 minus 459. That comes out to be negative 664, and we have defined that western direction as being negative here. So if that's the momentum change, then that also is the impulse delivered by Jerome to the running back. So the answer to part D is also 660 kilograms times a meter per second in the same direction, west. Now if you wish, you could express the unit for impulse as a newton times a second, which is absolutely 100% equivalent to having a kilogram times a meter per second.